2014-11-12-Dimensionality-Reduction-of-X-Ray-Scattering-Intensity-data.html

---
layout: post
title: "Dimensionality Reduction of X-ray Scattering Data"
author: davidbrough1
date: 2014-10-15 1:45:22

markdownify: True
---

In this post we will provide the overall work flow for doing Principle Component Analysis on X-ray Scattering Data.

# X-ray Scattering Intensity Image

<a href="https://www.flickr.com/photos/73249669@N02/15083260160" title="SAXS by Abhiram Kannan, on Flickr"><img src="https://farm4.staticflickr.com/3918/15083260160_a469fcb334_z.jpg" width="640" height="640" alt="SAXS"></a>

**Scaled SAXS X-ray Intensity Plot**

A class called [ImageDimensionReducer](https://github.com/phelpsforpresident/MIC-XRD-Polymer/blob/gh-pages/python_scripts/image_dimension_reducer.py)
was created to dimensionality reduction on image such as X-ray scattering data and/or 2-point statistics. 

[Here](https://github.com/phelpsforpresident/MIC-XRD-Polymer/blob/gh-pages/python_scripts/test.py) is an example of
how the class is used. It takes in an dimensionality reduction class from [sklearn](http://scikit-learn.org/stable/modules/classes.html#module-sklearn.decomposition)
and uses it to create a low dimensional representation the images loaded.

Below is an example of a plot the X-ray scattering data from one sample reduced using PCA.


![PCA Image](data:image/png;base64,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" />)


**PCA SAXS X-ray Intensity Plots for one Sample**